<i>H</i>₂ and mixed <i>H</i>₂/<i>H</i>_∞ Stabilization and Disturbance Attenuation for Differential Linear Repetitive Processes

Repetitive processes are a distinct class of two-dimensional systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. A systems theory for them cannot be obtained by direct extension of existing techniques from standard (termed 1-D here) or, in many cases, two-dimensional (2-D) systems theory. Here, we give new results towards the development of such a theory in H2 and mixed H2/H∞ settings. These results are for the sub-class of so-called differential linear repetitive processes and focus on the fundamental problems of stabilization and disturbance attenuation

Magnetic Trapping of Cold Bromine Atoms

Magnetic trapping of bromine atoms at temperatures in the milliKelvin regime is demonstrated for the first time. The atoms are produced by photodissociation of Br$_2$ molecules in a molecular beam. The lab-frame velocity of Br atoms is controlled by the wavelength and polarization of the photodissociation laser. Careful selection of the wavelength results in one of the pair of atoms having sufficient velocity to exactly cancel that of the parent molecule, and it remains stationary in the lab frame. A trap is formed at the null point between two opposing neodymium permanent magnets. Dissociation of molecules at the field minimum results in the slowest fraction of photofragments remaining trapped. After the ballistic escape of the fastest atoms, the trapped slow atoms are only lost by elastic collisions with the chamber background gas. The measured loss rate is consistent with estimates of the total cross section for only those collisions transferring sufficient kinetic energy to overcome the trapping potential

Control and Filtering for Discrete Linear Repetitive Processes with H infty and ell 2--ell infty Performance

Repetitive processes are characterized by a series of sweeps, termed passes, through a set of dynamics defined over a finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This can lead to oscillations which increase in amplitude in the pass to pass direction and cannot be controlled by standard control laws. Here we give new results on the design of physically based control laws for the sub-class of so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control. The main contribution is to show how control law design can be undertaken within the framework of a general robust filtering problem with guaranteed levels of performance. In particular, we develop algorithms for the design of an H? and $\ell_{2}–\ell_{\infty}$ dynamic output feedback controller and filter which guarantees that the resulting controlled (filtering error) process, respectively, is stable along the pass and has prescribed disturbance attenuation performance as measured by $H_{\infty}$ and $\ell_{2}$–$\ell_{\infty}$ norms

Controlling the Momentum Current of an Off-resonant Ratchet

We experimentally investigate the phenomenon of a quantum ratchet created by exposing a Bose-Einstein Condensate to short pulses of a potential which is periodic in both space and time. Such a ratchet is manifested by a directed current of particles, even though there is an absence of a net bias force. We confirm a recent theoretical prediction [M. Sadgrove and S. Wimberger, New J. Phys. \textbf{11}, 083027 (2009)] that the current direction can be controlled by experimental parameters which leave the underlying symmetries of the system unchanged. We demonstrate that this behavior can be understood using a single variable containing many of the experimental parameters and thus the ratchet current is describable using a single universal scaling law.Comment: arXiv admin note: substantial text overlap with arXiv:1210.565

Array concepts for solid-state and vacuum microelectronics millimeter-wave generation

The authors have proposed that the increasing demand for contact watt-level coherent sources in the millimeter- and submillimeter-wave region can be satisfied by fabricating two-dimensional grids loaded with oscillators and multipliers for quasi-optical coherent spatial combining of the outputs of large numbers of low-power devices. This was first demonstrated through the successful fabrication of monolithic arrays with 2000 Schottky diodes. Watt-level power outputs were obtained in doubling to 66 GHz. In addition, a simple transmission-line model was verified with a quasi-optical reflectometer that measured the array impedance. This multiplier array work is being extended to novel tripler configurations using blocking barrier devices. The technique has also been extended to oscillator configurations where the grid structure is loaded with negative-resistance devices. This was first demonstrated using Gunn devices. More recently, a 25-element MESFET grid oscillating at 10 GHz exhibited power combining and self-locking. Currently, this approach is being extended to a 100-element monolithic array of Gunn diodes. This same approach should be applicable to planar vacuum electron devices such as the submillimeter-wave BWO (backward wave oscillator) and vacuum FET